Geodesic
Crossing Numbers of Beyond-Planar Graphs Revisited
Journal of Graph Algorithms and Applications, Tome 26 (2022) no. 1, pp. 149-170.

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Graph drawing beyond planarity focuses on drawings of high visual quality for non-planar graphs which are characterized by certain forbidden (edge) crossing configurations. A natural criterion for the quality of a drawing is the number of edge crossings. The question then arises whether beyond-planar drawings have a significantly larger crossing number than unrestricted drawings. Chimani et al. [GD'19] gave bounds for the ratio between the crossing number of three classes of beyond-planar graphs and the unrestricted crossing number. In this paper we extend their results to the main currently known classes of beyond-planar graphs characterized by forbidden edge configurations and answer several of their open questions.
DOI : 10.7155/jgaa.00586
Keywords: Crossing Numbers, Beyond Planarity, Crossing Ratios 
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Nathan van Beusekom; Irene Parada; Bettina Speckmann. Crossing Numbers of Beyond-Planar Graphs Revisited. Journal of Graph Algorithms and Applications, Tome 26 (2022) no. 1, pp. 149-170. doi : 10.7155/jgaa.00586. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00586/

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